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The Ellsberg paradox: A challenge to quantum decision theory?

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  • Ali al-Nowaihi
  • Sanjit Dhami

Abstract

We set up a simple quantum decision model of the Ellsberg paradox. We find that the matching probabilities that our model predict are in good agreement with those empirically measured by Dimmock et al. (2015). Our derivation is parameter free. It only depends on quantum probability theory in conjunction with the heuristic of insufficient reason. We suggest that much of what is normally attributed to probability weighting might actually be due to quantum probability.

Suggested Citation

  • Ali al-Nowaihi & Sanjit Dhami, 2016. "The Ellsberg paradox: A challenge to quantum decision theory?," Discussion Papers in Economics 16/08, Division of Economics, School of Business, University of Leicester.
  • Handle: RePEc:lec:leecon:16/08
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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp16-08.pdf
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    References listed on IDEAS

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    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    3. Khalmetski, Kiryl & Ockenfels, Axel & Werner, Peter, 2015. "Surprising gifts: Theory and laboratory evidence," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 163-208.
    4. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    5. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    6. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    7. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    8. John D. Hey & Gianna Lotito & Anna Maffioletti, 2018. "The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 8, pages 189-219, World Scientific Publishing Co. Pte. Ltd..
    9. Chow, Clare Chua & Sarin, Rakesh K, 2001. "Comparative Ignorance and the Ellsberg Paradox," Journal of Risk and Uncertainty, Springer, vol. 22(2), pages 129-139, March.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. French, Kenneth R & Poterba, James M, 1991. "Investor Diversification and International Equity Markets," American Economic Review, American Economic Association, vol. 81(2), pages 222-226, May.
    12. Stephen G. Dimmock & Roy Kouwenberg & Peter P. Wakker, 2016. "Ambiguity Attitudes in a Large Representative Sample," Management Science, INFORMS, vol. 62(5), pages 1363-1380, May.
    13. Anna Conte & John D. Hey, 2018. "Assessing multiple prior models of behaviour under ambiguity," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 7, pages 169-188, World Scientific Publishing Co. Pte. Ltd..
    14. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    15. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    16. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    17. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    18. Curley, Shawn P. & Yates, J. Frank & Abrams, Richard A., 1986. "Psychological sources of ambiguity avoidance," Organizational Behavior and Human Decision Processes, Elsevier, vol. 38(2), pages 230-256, October.
    19. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324.
    20. Maurice Obstfeld & Kenneth Rogoff, 2001. "The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?," NBER Chapters, in: NBER Macroeconomics Annual 2000, Volume 15, pages 339-412, National Bureau of Economic Research, Inc.
    21. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    22. David K Levine, 2005. "Quantum Games Have No News For Economics," Levine's Working Paper Archive 618897000000001000, David K. Levine.
    23. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    24. Stefan Trautmann & Ferdinand Vieider & Peter Wakker, 2008. "Causes of ambiguity aversion: Known versus unknown preferences," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 225-243, June.
    25. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    26. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    27. Clare Chua Chow & Rakesh Sarin, 2002. "Known, Unknown, and Unknowable Uncertainties," Theory and Decision, Springer, vol. 52(2), pages 127-138, March.
    28. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
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    Cited by:

    1. Mengxing Wei & Ali al-Nowaihi & Sanjit Dhami, 2017. "Can quantum decision theory explain the Ellsberg paradox?," Discussion Papers in Economics 17/07, Division of Economics, School of Business, University of Leicester.
    2. Ali al-Nowaihi & Sanjit Dhami & Mengxing Wei, 2018. "Quantum Decision Theory and the Ellsberg Paradox," CESifo Working Paper Series 7158, CESifo.

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    More about this item

    Keywords

    Quantum probability; Ellsberg paradox; probability weighting; matching probabilities; projective expected utility; projective prospect theory;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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